Question

rita is driving her car on a business trip. she knows she will drive for at least 106 kilometers on the trip. also, she will drive for at most 130 kilometers on the trip (so that her company can cover her gas expenses). she has 4 days left on the trip. let x be the number of kilometers per day she will drive for these 4 days. (suppose she will decide to drive the same distance each day.) she has already driven the car for 50 kilometers on the trip.
(a) find the possible numbers of kilometers per day she will drive. write your answer as a compound inequality solved for x.
(b) on the number line below, graph the solution that represents the possible numbers of kilometers per day she will drive.

Explanation:

Step1: Set up total distance lower bound

Total distance: $50 + 4x \geq 106$

Step2: Solve lower bound for x

Subtract 50: $4x \geq 106 - 50$
$4x \geq 56$
Divide by 4: $x \geq 14$

Step3: Set up total distance upper bound

Total distance: $50 + 4x \leq 130$

Step4: Solve upper bound for x

Subtract 50: $4x \leq 130 - 50$
$4x \leq 80$
Divide by 4: $x \leq 20$

Step5: Combine into compound inequality

Combine the two results: $14 \leq x \leq 20$

Step6: Graph the solution on number line

1. Locate 14 and 20 on the number line.
2. Plot closed (filled) dots at 14 and 20 (since the inequality includes equality).
3. Draw a solid line segment connecting the two dots to show all values between them are included.

Answer:

(a) $\boldsymbol{14 \leq x \leq 20}$
(b) On the number line:

• Place a filled dot at 14, a filled dot at 20, and shade the region between these two points.